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 ==== Upcoming talks ====  ==== Upcoming talks ==== 
  
-**April 28 2026:  [[https://sites.google.com/ug.uchile.cl/espinoza|Bastiàn Espinoza]** //The Thue-Morse word in base 3/2//+To be scheduled later 
 + 
 +<del>**July 7 2026: Delaram Moradi**</del> 
 + 
 +==== Past talks 2026 ==== 
 +**June 23 2026: [[https://arxiv.org/search/math?searchtype=author&query=Cloitre,+B|Benoit Cloitre]]** //The Thue-Morse Transform// 
 + 
 +{{ seminar2026:20260623cloitre.pdf |slides}} 
 + 
 +{{ seminar2026:20260623cloitre.mp4 |video of the talk}} 
 + 
 + 
 + 
 +We define a transform $T$ on binary words. Given a binary word, we use the positions of its zeros and ones to build a new binary word. Applied to the alternating word $a_0 = 0101\ldots$, the transform gives the Thue-Morse word. We then study the orbit $a_m = T^m(a_0)$, together with the sequences $u_m$ and $v_m$ giving the positions of the ones and the zeros in $a_m$. We obtain an explicit formula for $a_m(n)$ in terms of the binary digits of $n$ and $m-1$. From this formula we derive Prouhet-Tarry-Escott identities, composition formulas that generalize the identities for evil and odious numbers, and a recurrence formula for the factor complexity of $a_m$. We end with a few directions, such as applying the transform to the Fibonacci word, which yields the Fibonacci-Thue-Morse word.  
 + 
 + 
 +**June 9 2026:  [[https://kmlinux.fjfi.cvut.cz/~balkolub/| Ľubomíra Dvořáková]]** //Attractors of sequences coding beta-integers// 
 + 
 +{{ seminar2026:20260609dvorakova.pdf |slides}} 
 + 
 +{{ seminar2026:20260609dvorakova.mp4 |video of the talk}} 
 + 
 + 
 + 
 +String attractor is an intensively studied object in Combinatorics on Words. 
 +In our talk, we will recall known results and also some previously used techniques. 
 +We will then describe minimal string attractors of prefixes of simple Parry sequences. 
 +These sequences form a coding of distances between consecutive beta-integers in numeration systems with a real base beta. 
 +Simple Parry sequences have been recently studied from this point of view and (not necessarily minimal) attractors of their prefixes have been described and a conjecture that attractors of alphabet size should be sufficient was stated. We prove this conjecture. Moreover, we provide attractors of prefixes of some particular form of binary non-simple Parry sequences. 
 + 
 + 
 +**May 12 2026: [[https://www-lmpa.univ-littoral.fr/~lvivion/|Léo Vivion]]** //New examples of words for which binomial complexities and subword complexity coincide// 
 + 
 +{{ seminar2026:20260512vivion.pdf |slides}} 
 + 
 +(The talk was not recorded at the speaker's request.) 
 + 
 +In 2015, Rigo and Salimov introduced a family of complexities that forms a scale between abelian complexity and factor complexity: the $k$-binomial complexities. In particular, they showed that Sturmian words satisfy the following remarkable combinatorial property: their $2$-binomial complexity is equal to their factor complexity. Since then, the only other known example satisfying this property is the Tribonacci word. 
 + 
 +In this talk, I will present some stability results for words whose $k$-binomial complexities coincide with their factor complexity, notably under letter deletion and a coloring operation. These stability properties allow to show that several well-known families of words also have their $2$-binomial complexity equal to their factor complexity. 
 + 
 + 
 +**April 28 2026:  [[https://sites.google.com/ug.uchile.cl/espinoza|Bastiàn Espinoza]]** //The Thue-Morse word in base 3/2// 
 + 
 +{{ seminar2026:20260428espinoza.pdf |slides}} 
 + 
 +{{ seminar2026:20260428espinoza.mp4 |video of the talk}} 
  
 A rich family of symbolic dynamical systems of low complexity is given by automatic sequences. These sequences are obtained by feeding the base-$k$ expansions of integers, for a fixed integer base $k$, into a finite automaton. A rich family of symbolic dynamical systems of low complexity is given by automatic sequences. These sequences are obtained by feeding the base-$k$ expansions of integers, for a fixed integer base $k$, into a finite automaton.
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 This is joint work with Julien Cassaigne, Michel Rigo, and Manon Stipulanti. This is joint work with Julien Cassaigne, Michel Rigo, and Manon Stipulanti.
  
-**May 12 2026: Léo Vivion** 
  
-**May 26 2026: Reem Yassawi** 
- 
-**June 9 2026:  [[https://kmlinux.fjfi.cvut.cz/~balkolub/| Ľubomíra Dvořáková]]** //Attractors of sequences coding beta-integers// 
- 
- 
-**July 7 2026: Delaram Moradi** 
- 
-==== Past talks 2026 ==== 
  
 **April 14 2026: Idrissa Kaboré** //On modulo-recurrence and window complexity in infinite words// **April 14 2026: Idrissa Kaboré** //On modulo-recurrence and window complexity in infinite words//